The present invention relates to the use of mechanical waves in the non-destructive testing of concrete.
Methods and devices are known that utilize the propagation and reception of mechanical waves within the acoustic and ultrasonic frequency ranges for testing characteristics of concrete.
Ultrasonic pulse velocity (UPV) test methods utilize piezoelectric transducers on opposite or adjacent sides of a concrete sample to determine the velocity of an ultrasonic signal transmitted through the concrete from one transducer to the other. Because defects in the concrete, such as voids or delaminations, can affect ultrasonic mechanical wave speed through the sample, the amount of variation in the signal velocity as measurements are taken across a concrete sample can indicate the presence of such defects or the presence of material such as metal reinforcing bars (rebar). Further, the UPV test method can be used to determine compressive strength. As should be understood, compressive strength is an estimate of the maximum amount of force that can be applied normally to a surface of the concrete sample without crushing the concrete.
ASTM C 597 describes a standard test method for utilizing pulse velocity through concrete. In one example of such method, respective transducers are disposed on opposite or adjacent sides of a concrete sample, such as a wall. Each transducer includes a piezoelectric element, as should be understood in this art, but other transducer crystals can be used. An impedance matching material, which is used to decrease the impedance difference between the piezoelectric material and the concrete, is disposed between each transducer's piezoelectric element and the concrete surface, and a gel is disposed between the impedance matching material and the concrete to fill air gaps. A control system excites one of the two narrowband transducers to impart a pulse of ultrasonic longitudinal mechanical waves (primary waves, or “p-waves”) into the concrete surface, at a frequency ranging from 50 kHz to 120 kHz. The pulse travels through the concrete and undergoes multiple reflections at occurrences of density variations within the concrete, for example due to delamination, air pockets, or rebar. A complex system of mechanical waves develops, including both p-waves and shear (or “s”) waves, and propagates through the concrete. P-waves travel faster than s-waves, and where the transducers are disposed are opposite sides of the concrete sample, the p-wave therefore first reaches the piezoelectric receiving transducer, which in turn converts the p-wave into an electrical signal. The transit time (TP) for the pulse to travel the known path length (L) is measured by the control system, and the longitudinal pulse velocity (Cp) is given by the following equation:
      C    p    =      L          T      p      
The accuracy of the velocity measured by this method is a function of the accuracy of the measured distance (L) between the transducers and the measured transit time (TP). For the pulse velocity operational mode, the programmable data acquisition has a sampling period (h), or transit time resolution, e.g. of 0.1 microseconds using a 10 MHz clock.
Shear waves also reach the opposite side of the concrete wall, and using a pair of shear wave transducers similarly disposed on opposite or adjacent sides of the concrete as the p-wave transducers, the s-wave transit time (Ts) is similarly measured. As should be understood in this art, s-wave transducers are piezoelectric devices configured to mechanically react in response to shear waves, thereby producing an electrical signal when the transducer is affected by a shear wave. Given the path length (L), the shear velocity (Cs) is given by the following equation:
      C    s    =      L          T      s      
The p-wave velocity (Cp) and shear velocity (Cs) are correlated to the Young's modulus (E), Poisson's ratio (ν), and density (ρ) of the material as determined by the following equations:
            C      p        =                            E          ⁡                      (                          1              -              v                        )                                                ρ            ⁡                          (                              1                -                                  2                  ⁢                  v                                            )                                ⁢                      (                          1              +              v                        )                                          C      s        =                  E                  2          ⁢                                          ⁢                      ρ            ⁡                          (                              1                +                v                            )                                          
The p-wave modulus (M) is correlated to the p-wave velocity (Cp) and density (ρ) of the material as determined by the following equation:M=ρCp2 
Using shear wave transducers, the shear modulus (G) can be correlated to shear velocity (Cs) and density (ρ) of the material as determined by the following equations:
      G    =          ρ      ⁢                          ⁢              C        s        2                  v    =                            M          -                      2            ⁢            G                                                2            ⁢            M                    -                      2            ⁢            G                              =                                    C            p            2                    -                      2            ⁢                          C              s              2                                                2          ⁢                      (                                          C                p                2                            -                              C                s                2                                      )                              
Thus, the Poisson's ratio (ν) can be determined without knowing the concrete density by measuring the p-wave velocity (Cp) and shear velocity (Cs). Once the Poisson's ratio (ν) is known, the control system calculates the Young's modulus (E) from the above equation, where density (ρ) is known from empirical destructive (stress/strain) testing. For conventional concrete from 200 psi to 3,000 psi, the compressive strength (σ) can be calculated from the following equation:E=0.043ρ1.5√{square root over (σ)}
Where density (ρ) is in units of kg/m′, and Young's modulus (E) and compressive strength (σ) are in MPa, the above equation is applicable to twenty-eight day compressive strength, and the following adaption of the American Concrete Institute (ACI) equation can be used, with the value of the proportionality constant (k) determined by curve fitting experimental data:E=k√{square root over (σ)}
The American Concrete Institute (ACI) Committee 318 recommends a model to predict the modulus of elasticity for a wide range of concrete compressive strengths from 200 psi to 3,000 psi, although overestimating the modulus of elasticity for compressive strength over 6,000 psi [ACI 318-11].E=0.043ρ1.5√{square root over (σ)}                where:        E=modulus of elasticity in MPa        ρ=density in kg/m3         σ=compressive strength in MPaE=4.38ρ1.5σ0.75         where:        E=modulus of elasticity in psi (English)        ρ=density in pcf or lb/ft3 (English)        σ=compressive strength in psi (English)        
The ACI Committee 363 recommends a model for higher strength concretes ranging from 3,000 psi to 12,000 psi [ACI 363R-92].E=3320√{square root over (σ)}+6900                where:        E=modulus of elasticity in MPa        ρ=density in kg/m3=2323 kg/m3         σ=compressive strength in MPaE=(40000√{square root over (σ)}+1.0×106)(ρ/145)1.5         where:        E=modulus of elasticity in psi (English)        ρ=density in pcf or lb/ft3 (English)=145 lb./ft3         σ=compressive strength in psi (English)        
The Architectural Institute of Japan (AU) recommends an equation to predict the modulus of elasticity for high-strength concretes ranging from 2,900 psi to 23,200 psi [Tomosawa, et al 1990]. The AIJ equation expresses the modulus of elasticity (E) as a function of compressive strength (σ), and density (ρ):E=k1486σ1/3ρ2                 where:        E=modulus of elasticity in MPa        ρ=density in kg/m3         σ=compressive strength in MPa        k=k1k2         k1=correction factor corresponding to coarse aggregates        k2=correction factor corresponding to mineral admixtures        
Compressive strength may also be determined by acoustic attenuation or relative amplitude, which measures the attenuation of an acoustic wave by observing the ratio of the wave amplitudes. As ultrasonic waves pass through materials, attenuation is caused by beam divergence (distance effect), absorption (heat dissipation), and scattering. Scattering is the only form of attenuation affected by the characteristics of the materials through which the waves pass, as well as the degree of inhomogeneity and frequency of the transducer. Attenuation caused by scattering (αs) is given by:
      α    s    ∝      {                                                      1              ⁢                              /                            ⁢              D              ⁢                                                          ⁢              for              ⁢                                                          ⁢              diffusion              ⁢                                                          ⁢              range              ⁢                                                          ⁢              λ                        ≤            D                                                                                          Df                2                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              stochastic              ⁢                                                          ⁢              range              ⁢                                                          ⁢              λ                        ≈            D                                                                                          D                3                            ⁢                              f                4                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              Raleigh              ⁢                                                          ⁢              range              ⁢                                                          ⁢              λ                        ⪢            D                              where f is the wave frequency, λ is the wavelength, and D is the average inhomogeneity in concrete. D may also be the void or aggregate size. For λ much greater than D, concrete strength is related exponentially with the wave attenuation.
Porosity is the main factor influencing strength of a brittle material such as concrete. Several models that relate strength to porosity exist, but the most common is the exponential model:K=K0e−kp where K0 is the strength at zero porosity, P is the fractional porosity, and k is a constant that depends on the system being studied.
Techniques for determining ultrasonic attenuation include placement of receiving and transmitting transducers on opposite or adjacent sides of a concrete sample. Typically, the use of adjacent sides is not possible because the amplitude of the pressure and the torsion waves are difficult to determine. However, when thickness of the structure is known, it may be possible to utilize an impulse reflected off of the opposing surface of the concrete sample, assuming a sufficiently high input signal.
When porosity is not known, the relative amplitude (β) can be correlated to the fractional porosity (P) for a specific condition, as shown by the following relationship between strength (K) and relative amplitude (β):K=e5.2115−0.1444β
The equation above is applicable to concrete with a moisture content of 3-4%, an age of ninety days, made from crushed granite aggregate with a maximum size of twenty mm, cured by immersing in water for twenty-eight days, and measured by the direct technique (receiving and transmitting transducers on opposing sides of the concrete sample) at 150 mm beam path distance without reinforcement bars. The relative amplitude decreases as the strength is increased. While the above equation is an example, such a relationship between strength and relative amplitude can be drawn from empirical testing.
When an impulse is transmitted through a material, the relative amplitude (β) is given by:
  β  =      20    ⁢                  ⁢          log      ⁡              (                              A            ps                                A            p                          )            where Aps is the pressure wave amplitude after the arrival of the torsional wave, and Ap is the pressure wave amplitude. Since the relative amplitude method sends an impulse through the concrete, it might also be used to correlate the size, type, and stiffness of any reinforcing fibers. This correlation is determined by sending impulses at various frequencies and analyzing the frequency response.
In some instances, only one side of the concrete sample may be accessible, such that thickness of a concrete sample is unknown. In such circumstances, or otherwise where it is desired to determine thickness of a concrete sample, the impact-echo method of determining concrete thickness may be used, as described in the ASTM C 1383 standard. The impact-echo test involves two modes of operation, both of which rely upon mechanical waves imparted to a concrete sample by an impact hammer. The impact hammer produces a mechanical impact on the concrete surface, generating multiple modes of vibration, including p-waves, s-waves and Rayleigh waves. The impact hammer includes a steel ball head in which is disposed a piezoelectric element that generates an electrical signal when the steel ball strikes the concrete sample. The impact hammer outputs this signal to a computer system, allowing the computer system to recognize that the test has begun and to therefore configure the system to receive the receiving transducer output.
The first part of the test determines p-wave speed, based on reception of the hammer-imparted p-wave detected by a pair of broadband transducers disposed on the same concrete surface at which the hammer imparts the mechanical wave. Both transducers may include piezoelectric elements that are coupled to the concrete surface. The receiving transducers are independently disposed on the concrete surface at a fixed distance, e.g. about 300 mm, apart. Although disposed on the concrete surface independently of each other, a spacer may be placed between them to fix the desired distance. The operator strikes a hammer on the concrete surface on the same line that includes the centers of the two receiving transducers, at a distance of 150+/−10 mm from the closest transducer, with an impact duration of 30+/−10 microseconds.
When the p-wave reaches the two piezoelectric receiver transducers, the transducers convert the mechanical energy to an electrical signal that is output to a computer. Upon reception of the signals from the receiving transducers, the computer determines the difference in time between the two signals, i.e. the p-wave's time of travel between the two receiving transducers, or (Δt). Since the distance (L) between the receiving transducers is known, the computer calculates p-wave speed (Cp) by dividing distance by travel time. P-wave speed in concrete is then converted to the apparent p-wave speed in a plate (Cp, plate=0.96 Cp).
The second part of the test determines the frequency of a standing wave generated by the hammer impact, i.e. the resonance frequency. A broadband transducer is manually disposed on the concrete surface, and the operator strikes the same concrete surface with the impact hammer near the transducer. The piezoelectric element at the impact hammer head outputs a signal from the hammer to the computer that triggers the computer to watch for a response from the broadband receiving transducer. The impact generates a p-wave that propagates into the concrete plate and reflects from the opposite surface. The return wave reflects, in turn, from the initial impact surface, and so on, giving rise to a transient thickness resonance. The broadband transducer converts the detected wave into an electrical signal that is output to the computer, which captures the output as a time domain waveform. The computer obtains a frequency domain signal through a windowing function and execution of a Fast Fourier transform. A Hamming window may be used to reduce ringing in the spectral values outside the windows. A sampling period may be two microseconds, using a 500 kHz clock and 1024 data points in the recorded waveform. The duration of the recorded waveform is 2048 microseconds, giving a spectral resolution of 488 Hz in the signal spectrum. There are 512 frequency channels, and the maximum sample frequency is 250 kHz. The computer displays 1024 samples in the time domain and 512 bins (250 kHz) in the frequency domain. The resonance frequency (f) appears as a peak in this waveform, which the software application identifies.
Thickness of the concrete plate is then given by the following equation:
  T  =            C              p        ,        plate                    2      ⁢      f      
The actual impact has a significant influence on the success of the impact-echo test. The estimate of the maximum frequency in the frequency domain excited is the inverse of the impact hammer's contact time at the concrete surface. Thus, a shorter contact time results in a higher range of frequencies contained in the pulse imparted into the concrete by the impact hammer, and the depth of the opposing surface (which may be the opposite surface of the concrete sample, or a defect or object located within the sample that creates an intermediate standing wave) which can be detected decreases according to the equation above. Short duration impacts are needed to detect opposing surfaces and defects that are near to the surface upon which the test is performed. Sansalone and Streett, “Impact-Echo: Nondestructive Evaluation of Concrete and Masonry,” (1997), provide an estimate of the maximum frequency (fmax=291/D) for a steel ball bearing of diameter D, and it is known for an impact hammer to utilize interchangeable steel and stainless steel balls that vary in diameter. As steel ball diameter increases in the impact hammer, so does maximum detectable thickness.
Depending upon knowledge of the characteristics of the concrete sample, the concrete density may be known.
The ultrasonic pulse echo method may be used on one side of a concrete sample to determine both thickness and concrete characteristics in the sample when only one side of the sample is available. In particular, this method may be used to detect internal features, such as the location and density of rebar. The principle is based on the measurement of the time interval between transmitting an ultrasonic impulse into the sample and receiving an echo. The transit time (T) of the pulse to traverse twice the path length to (L) is measured, and the longitudinal pulse velocity (Cp) is given by:
      C    p    =            2      ⁢      L        T  
Ultrasound is highly attenuated in concrete, and for increasing thicknesses, it may therefore be difficult to effectively obtain an echo signal. Thus, to overcome the effects of wave scattering, and thus attenuation, caused by aggregates and air pores, the frequency of the ultrasound signal is typically low, and can be as low as 50 kHz.
To implement this method, two narrowband transducers are applied to the same side of the concrete sample, at a predetermined distance apart from each other. The computer system excites one of the two transducers, causing the transducer to impart a mechanical signal into the sample. The computer system is in communication with both the transmitting and receiving transducers, actuating the transmitting transducer and receiving the electrical signal from the receiving transducer. The signal received from the receiving transducer will include data describing both a surface wave and reflections. To remove the surface wave data, leaving the reflection data, the computer system applies a signal processing technique known as frequency-wave number filtering (FK filtering). FK filtering uses the slope of the data to selectively remove values that lie along a particular line (two dimensional filtering).
In essence, the pulse-echo method determines the time of flight of the mechanical pulse imparted into the concrete sample and reflected back from the opposing side of the sample or an intermediate object, such as rebar. By taking these measurements sequentially across a concrete sample, the most common detected distance is typically from the opposing sample side. Accordingly, anomalies of shorter distances that appear in the output data correspond to positions at which imbedded material may occur.